The sequence ≥nd of nth degree stochastic dominances for d-dimensional distribution functions is defined. It is shown that, under some regularity conditions, ≥nd implies ≥nd−1 for the (d−1) - dimensional marginals. Also some necessary conditions for ≥nd are established. These...

We consider two random vectors X and Y, such that the components of X are dominated in the convex order by the corresponding components of Y. We want to find conditions under which this implies that any positive linear combination of the components of X is dominated in the convex order by the...

A class of stochastic orders is defined on the set of bivariate distribution functions. This class of orders is linearly orderable by inclusion. A family of utility functions, coherent with each of the stochastic orders previously defined, is determined. These utility functions represent...